In theoretical physics, an M2-brane, is a spatially extended mathematical object that appears in string theory and in related theories (e.g. M-theory, F-theory). In particular, it is a solution of eleven-dimensional supergravity which possesses a three-dimensional world volume.
The M2-brane solution can be found by requiring
(
P
o
i
n
c
a
r
e
)
3
×
S
O
(
8
)
symmetry of the solution and solving the supergravity equations of motion with the p-brane ansatz. The solution is given by a metric and three-form gauge field which, in isotropic coordinates, can be written as
d
s
M
2
2
=
(
1
+
q
r
6
)
−
2
3
d
x
μ
d
x
ν
η
μ
ν
+
(
1
+
q
r
6
)
1
3
d
x
i
d
x
j
δ
i
j
F
i
μ
1
μ
2
μ
3
=
ϵ
μ
1
μ
2
μ
3
∂
i
(
1
+
q
r
6
)
−
1
,
μ
=
1
,
…
,
3
i
=
4
,
…
,
11
,
where
η
is the flat-space metric and the distinction has been made between world volume
x
μ
and transverse
x
i
coordinates. The constant
q
is proportional to the charge of the brane which is given by the integral of
F
over the boundary of the transverse space of the brane.
